An algorithm for computing parametric order bases for univariate polynomial matrices with parameters is first presented in this paper. Starting from the non-parametric univariate polynomial matrix, our key idea is to construct a special module and module order. Then based on \Gr basis theory for modules, we present that the order basis can be obtained by computing a minimal \Gr basis for this module under this order. Further, we extend the definition of the order basis to the parametric polynomial matrix, and give the concept of comprehensive order basis systems. More importantly, the method based on \Gr bases for modules can be naturally generalized to the parametric case by means of comprehensive \Gr systems for modules. As a consequence, we design a new algorithm for computing comprehensive order basis systems.The proposed algorithm has been implemented on the computer algebra system Singular and Maple.